Surrogate modeling for physical fields of heat transfer processes based on physics-informed neural network

doi:10.11949/0438-1157.20201879

Abstract

Abstract:

By constructing structured deep neural network architecture, physics-informed neural networks (PINN) can be trained to solve supervised learning tasks with limited amount of boundary data while effectively integrating any given laws of physics described by general nonlinear partial differential equations (i.e., Navier-Stokes equation). However, the effect of PINN training is closely related to how the boundary conditions are set. In this work, two 2-D steady-state heat transfer problems, namely heat conduction model with internal heat source and convection heat transfer equation between plates are taken as examples. Two surrogate models are trained based on PINN by using two setting methods of soft boundary and hard boundary. The trained surrogate models are used to predict the output of temperature fields, which are verified and compared with the simulated data. The comparison results show that the prediction ability of PINN based on hard boundary is superior to the rival.

Key words: neural networks, laws of physics, nonlinear partial differential equations, boundary setting, surrogate model, heat transfer, prediction

摘要：

物理信息的神经网络（PINN）通过构建结构化的深度神经网络体系，可以有效地耦合基于物理定律的非线性偏微分方程组（如Navier-Stokes方程），能够在较少量的边界数据条件下解决监督学习问题。但是，PINN训练效果与边界条件的设置方式密切相关。本工作以具有内热源的二维稳态导热方程和平板间二维稳态对流传热方程为案例，基于软边界和硬边界两种设定方法构建PINN。将训练所得到的代理模型预测温度场输出，并将其与软件模拟结果进行验证分析，结果表明硬边界PINN代理模型预测能力较优。

关键词: 神经网络, 物理定律, 非线性偏微分方程组, 边界设置, 代理模型, 传热, 预测

CLC Number:

LU Zhibin, QU Jinghui, LIU Hua, HE Chang, ZHANG Bingjian, CHEN Qinglin. Surrogate modeling for physical fields of heat transfer processes based on physics-informed neural network[J]. CIESC Journal, 2021, 72(3): 1496-1503.

陆至彬, 瞿景辉, 刘桦, 何畅, 张冰剑, 陈清林. 基于物理信息神经网络的传热过程物理场代理模型的构建[J]. 化工学报, 2021, 72(3): 1496-1503.

Figures/Tables 7

Fig.1 PINN structure diagram

Fig.2 Comparsion of temperature fields predicted by soft PINN, hard PINN, and COMSOL simulation

Fig.3 Comparsion of temperature contours predicted by soft PINN

Fig.4 Comparsion of temperature contours predicted by hard PINN

Fig.5 Geometric diagram of the flat plate

Fig.6 Comparsion of temperature fields predicted by hard PINN and COMSOL simulation

Fig.7 Comparsion of temperature contours predicted by hard PINN (red line) and COMSOL simulation (black line)

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